{"id":18104,"date":"2020-04-18T23:10:51","date_gmt":"2020-04-18T23:10:51","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/?post_type=chapter&#038;p=18104"},"modified":"2024-04-30T23:15:08","modified_gmt":"2024-04-30T23:15:08","slug":"summary-graphing-linear-inequalities","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/chapter\/summary-graphing-linear-inequalities\/","title":{"raw":"Summary: Graphing Linear Inequalities","rendered":"Summary: Graphing Linear Inequalities"},"content":{"raw":"<h2>Key Concepts<\/h2>\r\n<strong>Verifying a solution of a Linear Inequality <\/strong>The ordered pair [latex](x,y)[\/latex] is a solution of a linear inequality if, when the values are plugged into the linear inequality, the statement remains true.\r\n\r\n<strong>Graphing Linear Inequalities\u00a0\u00a0<\/strong>To graph an inequality,\r\n<ul>\r\n \t<li>Graph the related boundary line. Replace the &lt;, &gt;, \u2264 or \u2265 sign in the inequality with = to find the equation of the boundary line.<\/li>\r\n \t<li>Identify at least one ordered pair on either side of the boundary line and substitute those [latex](x,y)[\/latex] values into the inequality. Shade the region that contains the ordered pairs that make the inequality a true statement.<b>\u00a0<\/b><\/li>\r\n \t<li>If points on the boundary line are solutions, then use a solid line for drawing the boundary line. This will happen for \u2264 or \u2265 inequalities.<\/li>\r\n \t<li>If points on the boundary line aren\u2019t solutions, then use a dotted line for the boundary line. This will happen for &lt; or &gt; inequalities.<\/li>\r\n<\/ul>","rendered":"<h2>Key Concepts<\/h2>\n<p><strong>Verifying a solution of a Linear Inequality <\/strong>The ordered pair [latex](x,y)[\/latex] is a solution of a linear inequality if, when the values are plugged into the linear inequality, the statement remains true.<\/p>\n<p><strong>Graphing Linear Inequalities\u00a0\u00a0<\/strong>To graph an inequality,<\/p>\n<ul>\n<li>Graph the related boundary line. Replace the &lt;, &gt;, \u2264 or \u2265 sign in the inequality with = to find the equation of the boundary line.<\/li>\n<li>Identify at least one ordered pair on either side of the boundary line and substitute those [latex](x,y)[\/latex] values into the inequality. Shade the region that contains the ordered pairs that make the inequality a true statement.<b>\u00a0<\/b><\/li>\n<li>If points on the boundary line are solutions, then use a solid line for drawing the boundary line. This will happen for \u2264 or \u2265 inequalities.<\/li>\n<li>If points on the boundary line aren\u2019t solutions, then use a dotted line for the boundary line. This will happen for &lt; or &gt; inequalities.<\/li>\n<\/ul>\n","protected":false},"author":253111,"menu_order":25,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"305947b72e4d461ea5bda8516ea1aa9a ","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-18104","chapter","type-chapter","status-publish","hentry"],"part":8524,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/18104","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/wp\/v2\/users\/253111"}],"version-history":[{"count":3,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/18104\/revisions"}],"predecessor-version":[{"id":18108,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/18104\/revisions\/18108"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/parts\/8524"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/18104\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/wp\/v2\/media?parent=18104"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapter-type?post=18104"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/wp\/v2\/contributor?post=18104"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/wp\/v2\/license?post=18104"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}